components of the integrated circuits

components of the integrated circuits

In the last decades, the components of the integrated circuits developed in speed and efficiency, and shrunk to reach to the nanoscale[1]. The classical mechanics cannot deal with the nanoscale; whereas, the quantum mechanics can study the components in nanoscale. The electronic transport can be understood by using the quantum mechanics. Nanowire is one of the electronic components in nanoscale[2]. Nanowires are one-dimensional nanostructure. This means it has a very small width compared to its length with a small diameter. The nanowires provide a confinement along two directions while the third direction is along which a conduction electron move[3] [4]. The properties of nanowires vary depending on the methods of synthesis even if they made of the same material[4] [5]. There are two regimes for electronic transport phenomena in nanowires, the first one is ballistic transport, which occur when electron travels without scattering and the mean path of electron is larger than the length of wire. Whereas, in the second regime the length of wire is larger than the mean path of electron, that undergoes scattering, This kind of transport is called diffusive transport [4] [6]. There are three length scales characterize the behavior of electronic transport nanowires, include length of diameter of nanowires, de Broglie wavelength of electron and mean path of electron[4]. The conductance quantization phenomena occur when the diameter of nanowire is in the range of 0.5 nm. Therefore, we can observe the conductance quantization for short and narrow nanowires[4]. The nanowires have band structure different from their bulk counterparts, which can be considered as a promising platform for thermoelectric applications[4] [7]. There are many different applications of nanowires that extend in all fields and all aspects of the life[4] [8]. The nanowires used in electronic devices, and they can used in electronic circuit as a component like diodes or transistors[9]. The nanowires have a small diameter so that they can used in flat panel displays[4]. Additionally, nanowires contained in memory cells, and it can used in information storage, magnetic storage, light emitting diode, solar cells, photovoltaics, sensor for chemical, biochemical, electrochemical and photoelectrochemical; the nanowires can be used as barcode tags for optical readout[4].

The applications of nanowires rapidly increased; so that, it is necessary to studying and understanding the electronic transmission in the nanowires[2].

• Literature review

The nanowire transmission properties can be obtained by applying dynamic or static methods. There are different methods to solve the time-independent Schrödinger equation to obtaining the total transmission coefficients. One of them is discretizing the wave function and the potential by taking a set of basis functions for every point in the mesh, this method called the finite element discretization method, it is numerical solution[10]. Another one is the mode-matching method, which based on divides the scattering region into separate regions; with analytical solution for each of them[11]. Another method is Green’s function method, it used to solve the Schrodinger equation in [12]. The total transmission coefficients can also obtained directly by solving the time-dependent Schrodinger equation, this method called the direct method[2] [13]. Another method is scattering matrix method which depends on splitting the structure into layers[14]. In this thesis, the R-matrix method used to calculate the transmission coefficients. The R-matrix method introduced in 1947 by Wigner-Eisenbud[15]. This technique based on calculating the Wigner-Eisenbud functions. The R-matrix method was implemented on many different problems, such as nuclear physics[15], designing the transistor in nanoscale[16] [17] and nanoscale transport problems[18] [19] [20]. The R-matrix method chosen because it has several advantages: the first one is that when the scattering potential suddenly changes or the system’s structure varies , the R-matrix scheme is not affected [21]; the second one , the R-matrix method is numerically very efficient compared with the other methods; third, is the R-matrix method can apply on nanostructures of higher-dimensional ,and in the case of complex geometry ,and when the potential is nonseparaple[22]; the last one is the zeros of the Wigner-Eisenbud functions have the same number of self-consistent procedure[19].

Previously, the effects of ordered spatial distribution of impurities was studied for two-dimension nanoscale in rectangular coordinates[23]; also the transport properties of random distribution of scattering centers was studied in rectangular coordinates through two-dimension nanoribbon[24].

• The aim of the work

The aim of this work is computation the transmission coefficients for an electron scatter by the inner potential inside nanowire. These coefficients are evaluated by the Wigner-Eisenbud functions; and using the R-matrix method. This research project concentrates specially on an inhomogeneous material distributed at scattering zone, which causes irregular potential. In this work, the transmission coefficients calculated for nanowire in one-dimension and two-dimension cylindrical coordinates.